title: A new mathematical equation relating activation energy to bond angle and distance: A key for understanding the role of acceleration in lactonization of the trimethyl lock system.
abstract: AM1 semi-empirical molecular orbital and ab initio HF at the 6-31G level calculations for the lactonization processes of 12 different hydroxy acids (1a-1l) which differ in their structural features have been conducted. The calculations obtained reveal the following: (1) The rate-limiting step in the lactonization process is formation of a tetrahedral intermediate and not its collapse as was previously reported. (2) The rate-limiting step in both the acid-catalyzed and uncatalyzed lactonization is composed of two successive steps: approach of the hydroxyl toward the carbonyl carbon until it reaches a distance of 1.4 -1.5A, followed by proton transfer from the ether-type oxygen to one of the hydroxyls in the tetrahedral intermediate. Calculations of the activation energies for formation of the tetrahedral intermediate in the 12 hydroxy acids studied indicate: (1) A linear relationship exists between the change in enthalpic energy (E) and the ratio of the attack angle (nucleophilic-oxygen/carbonyl-carbon/alphalambdapietaalpha-carbon) to the distance (nucleophilic-oxygen/carbonyl-carbon) termed alpha/r; (2) The slope (S) of E vs. alpha/r plots depend on the nature of the hydroxy acids. Furthermore, plots of S values against the experimental rate values (log k(exp)) show a linear correlation with a high correlation coefficient. The combined results suggest that hydroxy acids with low S values have high k(exp) values due to enthalpic proximity effects.
authors.affiliation: College of Pharmacy, Al-Quds University, Abu-Dies, Jerusalem, Palestinian Territory. dr_karaman@yahoo.com
authors.forename: Rafik
authors.initials: R
authors.lastname: Karaman
mesh_terms: D000465:Algorithms; D002244:Carbon / Q000737:chemistry; D002384:Catalysis; D002934:Cinnamates / Q000737:chemistry; D004735:Energy Transfer; D006880:Hydroxy Acids / Q000737:chemistry*; D007783:Lactones / Q000737:chemistry*; D008433:Mathematics; D008697:Methane / Q000737:chemistry*; D008956:Models, Chemical; D015394:Molecular Structure; D010100:Oxygen / Q000737:chemistry; D011522:Protons; D013816:Thermodynamics
chemical_list: D002934:Cinnamates; D006880:Hydroxy Acids; D007783:Lactones; D011522:Protons; D002244:Carbon; D008697:Methane; D010100:Oxygen